Deep Learning Computed Tomography: Learning Projection-Domain Weights From Image Domain in Limited Angle Problems

In this paper, we present a new deep learning framework for 3-D tomographic reconstruction. To this end, we map filtered back-projection-type algorithms to neural networks. However, the back-projection cannot be implemented as a fully connected layer due to its memory requirements. To overcome this problem, we propose a new type of cone-beam back-projection layer, efficiently calculating the forward pass. We derive this layer's backward pass as a projection operation. Unlike most deep learning approaches for reconstruction, our new layer permits joint optimization of correction steps in volume and projection domain. Evaluation is performed numerically on a public data set in a limited angle setting showing a consistent improvement over analytical algorithms while keeping the same computational test-time complexity by design. In the region of interest, the peak signal-to-noise ratio has increased by 23%. In addition, we show that the learned algorithm can be interpreted using known concepts from cone beam reconstruction: the network is able to automatically learn strategies such as compensation weights and apodization windows.